Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method. Issue 1651 (2014)

• Record Type: Journal Article
• Authors: Ebrahimi, Alireza; Monavari, Mehran; Hochrainer, Thomas
• Is Part Of: MRS proceedings. Issue 1651:(2014)
• Publication Date: 2014
• Subjects: dislocations, -- microstructure, -- crystalline; Electrical engineering -- Congresses; Physics -- Congresses; Materials -- Research -- Congresses; Materials science -- Congresses; 620.11
• DOI: 10.1557/opl.2014.26
• Languages: English
• ISSNs: 0272-9172

Abstract

ABSTRACT: In the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.